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प्रश्न
Integrate the following with respect to x.
x log x
उत्तर
`int x log x "d"x = int "udv"`
`int "udv" = "uv" - int "vdu"`
`int x log x "d"x = (log x)(x^2/2) - int (x^2/2) ("d"x)/x`
= `x^2/2log - int ((x"d"x)/2)`
= `x^2/2 log x - 1/2 [x^2/2] + "c"`
= `x^2/2 [log x - 1/2] + "c"`
| Successive derivatives | Repeated Integrals |
|
Take u = log x `"du"/("d"x) = 1/x` du = `("d"x)/x` |
dv = x dx `int "dv" = int x "d"x` v = `x^2/2` |
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